If you are third party only, then a green card isn't strictly needed to provide mimumum cover in most EU countries.
However, as it should be free, then there are some benefits to getting one. Theres absolutely no point to not making a quick call to the insurers and asking for one, so do it.
for example, a green card information pack will probably include an "ASOF" which is a continetal insurance claim form. If you get involved in an accident, the foreign driver will have one, will fill theirs in for you, give you a copy, and before you know it, having signed it, you have inadvertently admitted liability in a legally binding document by the road side which cannot really be disputed. Every year we get people who dont understand the significance of the form being stitched up by foreign drivers as its known UK motorists don't understand.
If you have an ASOF in your car from the green card pack, at least your identical but in English form will help you out with exchanging details and agreeing at the scene what happened.
Also will be good advice in the pack such as if you have an accident in Spain, then without witnesses, or a police report, if a driver refuses tosign an asof and drives off, you cannot make a claim, as to a spanish insurer only an ASOF is "proof" their driver was involved.
Also, if you are tpf&t, a green card will at least cover you for theft and fire. If you are comp cover, then you really really need a Green card, as otherwise your insurance will not cover you for damage to the vehicle regardless of the premiums you pay and the cover you think you have.